David J. Platt

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All published works

Action	Title	Year	Authors
+ PDF Chat	The mean square of the error term in the prime number theorem	2021	Richard P. Brent David J. Platt Timothy S. Trudgian
+	Accurate estimation of sums over zeros of the Riemann zeta-function	2021	Richard P. Brent David J. Platt Timothy S. Trudgian
+ PDF Chat	Sign changes in the prime number theorem	2021	Thomas Morrill David J. Platt Tim Trudgian
+ PDF Chat	The Riemann hypothesis is true up to 3·1012	2021	David J. Platt Tim Trudgian
+ PDF Chat	A HARMONIC SUM OVER NONTRIVIAL ZEROS OF THE RIEMANN ZETA-FUNCTION	2020	Richard P. Brent David J. Platt Timothy S. Trudgian
+	The error term in the prime number theorem	2020	David J. Platt Timothy S. Trudgian
+	The mean square of the error term in the prime number theorem	2020	Richard P. Brent David J. Platt Timothy S. Trudgian
+ PDF Chat	Improved Bounds on Brun’s Constant	2020	David J. Platt Tim Trudgian
+	The mean square of the error term in the prime number theorem	2020	Richard P. Brent David J. Platt Timothy S. Trudgian
+	Sign changes in the prime number theorem.	2019	Thomas Morrill David J. Platt Tim Trudgian
+	The mean square of the error term in the prime number theorem	2019	David J. Platt Timothy S. Trudgian
+	Sign changes in the prime number theorem	2019	Thomas Morrill David J. Platt Tim Trudgian
+ PDF Chat	Fujii’s development on Chebyshev’s conjecture	2018	David J. Platt Tim Trudgian
+	Robin's inequality for 25-free integers and obstacles to analytic improvement	2018	David J. Platt Thomas Morrill
+	Robin's inequality for 20-free integers	2018	Thomas Morrill David J. Platt
+	The error term in the prime number theorem	2018	David J. Platt Tim Trudgian
+ PDF Chat	Turing’s Method for the Selberg Zeta-Function	2018	Andrew R. Booker David J. Platt
+	Improved bounds on Brun's constant	2018	David J. Platt Tim Trudgian
+	Fujii's development on Chebyshev's conjecture.	2018	David J. Platt Tim Trudgian
+	The error term in the prime number theorem	2018	David J. Platt Tim Trudgian
+	Fujii's development on Chebyshev's conjecture	2018	David J. Platt Tim Trudgian
+	Improved bounds on Brun's constant	2018	David J. Platt Tim Trudgian
+ PDF Chat	A conjectural extension of Hecke’s converse theorem	2017	Sandro Bettin Jonathan Bober Andrew R. Booker Brian Conrey Min Lee Giuseppe Molteni Thomas Oliver David J. Platt Raphael S. Steiner
+ PDF Chat	On the Sum of Two Squares and At Most Two Powers of 2	2017	David J. Platt Timothy S. Trudgian
+	On the sum of two squares and at most two powers of 2	2016	David J. Platt Tim Trudgian
+ PDF Chat	Isolating some non-trivial zeros of zeta	2016	David J. Platt
+ PDF Chat	Explicit Estimates: From Λ(<i>n</i>) in Arithmetic Progressions to Λ(<i>n</i>)/<i>n</i>	2016	David J. Platt Olivier Ramaré
+ PDF Chat	Diophantine quintuples containing triples of the first kind	2016	David J. Platt Timothy S. Trudgian
+ PDF Chat	On the sum of the square of a prime and a square-free number	2016	Adrian Dudek David J. Platt
+ PDF Chat	Zeroes of partial sums of the zeta-function	2016	David J. Platt Timothy S. Trudgian
+	On the sum of two squares and at most two powers of 2	2016	David J. Platt Tim Trudgian
+ PDF Chat	On the first sign change of $\theta (x) -x$	2015	David J. Platt Timothy S. Trudgian
+ PDF Chat	On Solving a Curious Inequality of Ramanujan	2015	Adrian Dudek David J. Platt
+	Numerical computations concerning the GRH	2015	David J. Platt
+	On a Theorem of Erd\H{o}s in Additive Number Theory	2015	Adrian Dudek David J. Platt
+	Linnik's approximation to Goldbach's conjecture, and other problems	2015	David J. Platt Timothy S. Trudgian
+	Diophantine quintuples containing triples of the first kind	2015	David J. Platt Tim Trudgian
+	There are no Diophantine quintuples containing triples of the first kind	2015	David J. Platt Tim Trudgian
+	Diophantine quintuples containing triples of the first kind	2015	David J. Platt Tim Trudgian
+	An improved explicit bound on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mo stretchy="false">\|</mml:mo><mml:mi>ζ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">\|</mml:mo></mml:math>	2014	David J. Platt Timothy S. Trudgian
+ PDF Chat	Computing $\pi (x)$ analytically	2014	David J. Platt
+	On the first sign change of $\theta(x) - x$	2014	David J. Platt Tim Trudgian
+	On Solving a Curious Inequality of Ramanujan	2014	David J. Platt Adrian Dudek
+	Linnik's approximation to Goldbach's conjecture, and other problems	2014	David J. Platt Tim Trudgian
+	An improved explicit bound on $\|\zeta(1/2 + it)\|$	2014	David J. Platt Tim Trudgian
+	Linnik's approximation to Goldbach's conjecture, and other problems	2014	David J. Platt Tim Trudgian
+	An improved explicit bound on $\|ζ(1/2 + it)\|$	2014	David J. Platt Tim Trudgian
+	On the first sign change of $θ(x) - x$	2014	David J. Platt Tim Trudgian
+	On Solving a Curious Inequality of Ramanujan	2014	David J. Platt Adrian Dudek
+	Numerical Verification of the Ternary Goldbach Conjecture up to 8.875·10<sup>30</sup>	2013	H. A. Helfgott David J. Platt
+	Explicit Upper Bounds for $\|L(1, \chi)\|$ when $\chi(3)=0$	2013	Sumaia Saad Eddin David J. Platt
+	Numerical Computations Concerning the GRH	2013	David J. Platt
+ PDF Chat	Explicit upper bounds for \|L(1, χ)\| when χ(3)=0	2013	David J. Platt Sumaia Saad Eddin
+	Numerical Verification of the Ternary Goldbach Conjecture up to 8.875e30	2013	H. A. Helfgott David J. Platt
+	Explicit Upper Bounds for $\|L(1, χ)\|$ when $χ(3)=0$	2013	Sumaia Saad Eddin David J. Platt
+	Numerical Computations Concerning the GRH	2013	David J. Platt
+	Computing $\pi(x)$ Analytically	2012	David J. Platt
+	Chern Character for Global Matrix Factorizations	2012	David J. Platt
+	Computing $π(x)$ Analytically	2012	David J. Platt
+	Computing degree-1 L-functions rigorously	2011	David J. Platt

Common Coauthors

Coauthor	Papers Together
Tim Trudgian	23
Timothy S. Trudgian	13
Adrian Dudek	5
Thomas Morrill	5
Richard P. Brent	5
Sumaia Saad Eddin	3
H. A. Helfgott	2
Andrew R. Booker	2
Giuseppe Molteni	1
Thomas Oliver	1
Sandro Bettin	1
Olivier Ramaré	1
Min Lee	1
Raphael S. Steiner	1
Jonathan Bober	1
Brian Conrey	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	A still sharper region where $\pi (x)-{\mathrm {li}}(x)$ is positive	2015	Yannick Saouter Timothy S. Trudgian Patrick Demichel	12
+ PDF Chat	On the difference π(x) - li(x)	1966	Robert S. Lehman	10
+ PDF Chat	Approximate formulas for some functions of prime numbers	1962	J. Barkley Rosser Lowell Schoenfeld	9
+	Improvements to Turing’s method	2011	Timothy S. Trudgian	8
+ PDF Chat	Artin's Conjecture, Turing's Method, and the Riemann Hypothesis	2006	Andrew R. Booker	8
+	Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x)	1975	J. Barkley Rosser Lowell Schoenfeld	8
+ PDF Chat	Isolating some non-trivial zeros of zeta	2016	David J. Platt	7
+	An improved upper bound for the argument of the Riemann zeta-function on the critical line II	2013	Timothy S. Trudgian	7
+	Some Calculations of the Riemann Zeta-Function	1953	Alan Turing	7
+	Explicit Bounds for Some Functions of Prime Numbers	1941	Barkley Rosser	7
+	Arb	2014	Fredrik Johansson	6
+	Multiplicative Number Theory	1980	H. Davenport	6
+ PDF Chat	Estimating $\pi (x)$ and related functions under partial RH assumptions	2015	Jan Büthe	6
+	The Theory of the Riemann Zeta-Function	1987	E. C. Titchmarsh D. R. Heath‐Brown	6
+ PDF Chat	Sharper bounds for the Chebyshev functions 𝜃(𝑥) and 𝜓(𝑥). II	1976	Lowell Schoenfeld	5
+	An improved explicit bound on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mo stretchy="false">\|</mml:mo><mml:mi>ζ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac><mml:mo>+</mml:mo><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">\|</mml:mo></mml:math>	2014	David J. Platt Timothy S. Trudgian	5
+ PDF Chat	Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic	2017	Fredrik Johansson	5
+ PDF Chat	The large sieve	1973	Hugh L. Montgomery R. C. Vaughan	5
+ PDF Chat	Numerical computations concerning the ERH	1993	Robert Rumely	5
+ PDF Chat	On the first sign change of $\theta (x) -x$	2015	David J. Platt Timothy S. Trudgian	5
+	Sur la distribution des nombres premiers	1901	Helge Koch	5
+	Computing degree-1 L-functions rigorously	2011	David J. Platt	5
+ PDF Chat	The Distribution of Prime Numbers	1933	A. E. Ingham	4
+	Multiplicative Number Theory I: Classical Theory	2006	Hugh L. Montgomery R. C. Vaughan	4
+	Explicit estimates of some functions over primes	2016	Pierre Dusart	4
+	Minor arcs for Goldbach's problem	2012	H. A. Helfgott	4
+ PDF Chat	Evaluation of Artin’s constant and the twin-prime constant	1961	John W. Wrench	4
+	On the error in reconstructing a non-bandlimited function by means of the bandpass sampling theorem	1967	Jerram L. Brown	4
+ PDF Chat	Changes of sign of the error term in the prime number theorem	2006	Hugh L. Montgomery Ulrike M. A. Vorhauer	4
+ PDF Chat	Computing π(x): An analytic method	1987	Jeffrey C. Lagarias Andrew Odlyzko	4
+	The mean square of the error term in the prime number theorem	2020	Richard P. Brent David J. Platt Timothy S. Trudgian	4
+ PDF Chat	Updating the error term in the prime number theorem	2015	Tim Trudgian	4
+	Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function	2015	Michael J. Mossinghoff Timothy S. Trudgian	4
+	Explicit zero density for the Riemann zeta function	2018	Habiba Kadiri Allysa Lumley Nathan Ng	3
+ PDF Chat	A zero density result for the Riemann zeta function	2013	Habiba Kadiri	3
+ PDF Chat	Computing the Principal Branch of log-Gamma	1997	D. E. G. Hare	3
+	Zero-free Regions for the Riemann Zeta Function	2024	Kevin Ford	3
+	An analytic method for bounding 𝜓(𝑥)	2017	Jan Büthe	3
+ PDF Chat	On Solving a Curious Inequality of Ramanujan	2015	Adrian Dudek David J. Platt	3
+ PDF Chat	Sharper bounds for the Chebyshev functions 𝜃(𝑥) and 𝜓(𝑥)	1975	J. Barkley Rosser Lowell Schoenfeld	3
+	On the Distribution of Zeros of the Riemann Zeta-Function	1970	Robert S. Lehman	3
+ PDF Chat	Prime sieves using binary quadratic forms	2003	A. O. L. Atkin Daniel J. Bernstein	3
+	Ramanujan’s Notebooks: Part V	1997	Bruce C. Berndt	3
+	Analytic computation of the prime-counting function	2004	Harold G. Diamond William F. Galway	3
+ PDF Chat	An improved upper bound for the error in the zero-counting formulae for Dirichlet $L$-functions and Dedekind zeta-functions	2014	Timothy S. Trudgian	3
+ PDF Chat	Über die Nullstellen der Riemannschen Zetafunktion	1916	Robin Backlund	3
+ PDF Chat	Explicit Estimates for the Riemann Zeta Function	2004	Yuanyou Furui Cheng S. W. Graham	3
+ PDF Chat	Computing 𝜋(𝑥): the Meissel-Lehmer method	1985	Jeffrey C. Lagarias Victor S. Miller Andrew Odlyzko	3
+ PDF Chat	On the exact number of primes less than a given limit	1959	D. H. Lehmer	3
+ PDF Chat	Corrigendum: “Sharper bounds for the Chebyshev functions 𝜃(𝑥) and 𝜓(𝑥). II” (Math. Comput. 30 (1976), no. 134, 337–360)	1976	Lowell Schoenfeld	3